Which calculation is easier for a computer?

Question

I have two problems and I want to know which one is easier to handle for a computer (running time, number of needed operations....):

Given matrix $A \in \mathbb{Z}^{m \times n}$ and vector $d \in \mathbb{Z}^m$

1. Find a vector y such that $y^TA=0, y\geq 0, y^Td>0$
2. Find a vector y such that $y^TA \in \mathbb{Z}^n, y^Td \notin \mathbb{Z}$

The expressions as $y \geq 0$ have to be understood componentwise. If it helps, the first one is called Farkas Lemma and the second one lattice analouge Farkas Lemma.

Thank you very much for your responses!